It is important in long-haul optical communications to realize high spectrum utilization efficiency and, accordingly, communication systems using multi-level modulated signals or polarization-multiplexed signals have been developed. Since coherent receiving systems can receive multi-level modulated signals and polarization-multiplexed signals, they have been used in a large number of communication systems in recent years. It is possible in the coherent receiving system to obtain the information not only on the amplitude of the received light but also on the phase of it because the received light is detected by a photodetector after having interfered with local oscillator light. Concerning the signal obtained by using the coherent receiving system, therefore, it is known that by means of the digital signal processing the signal degradation while transmitting can be compensated and the obtained signal can be demodulated. The digital signal processing technology mentioned above, therefore, has become important.
By using the digital signal processing technology, it is possible to compensate a received signal with a temporal spread of the optical signal occurring due to the polarization mode dispersion, for example. The polarization mode dispersion means a difference in the propagation velocity in an optical fiber transmission line between polarization modes which is caused by a deviation from an exact circle in a fiber, and the like. Phenomena having polarization dependence in a transmission line, such as polarization mode dispersion and polarization rotation, have frequency dependence and vary temporally due to a different kind of external action such as pressure applied to a fiber. It is necessary, therefore, to perform the digital signal processing adaptively in order to equalize received signals deteriorated by a factor with such temporal variation.
It is possible to perform adaptive equalization signal processing in the time domain by using a finite impulse response (FIR) filter. In optical communication technologies, a butterfly-structured FIR filter as shown in FIG. 9 is generally employed in order to equalize signals deteriorated by a factor dependent on the polarization. The coefficients of the FIR filter are adaptively adjusted by a feedback control based on the CMA (Constant Modulus Algorithm) method or the DDLMS (Decision Directed Least Mean Square) algorithm, for example.
An example of a method for controlling a butterfly-structured FIR filter is described in Non Patent Literature 1. As shown in FIG. 9, an X-polarization input EX(k) and a Y-polarization input EY(k) are input into a related butterfly-structured FIR filter 900, whose outputs EX(k) and EY(k) are expressed as follows:Ex(k)=hxxT·EX+hxyT·EY=Σm=0M−1[hxx(m)EX(k−m)+hxy(m)EY(k−m)]  (1)Ey(k)=hyxT·EX+hyyT·EY=Σm=0M−1[hyx(m)EX(k−m)+hyy(m)EY(k−m)]  (2)
Here, hxx=[hxx(0) . . . hxx(M−1)] and the like are tap coefficients of the FIR filter, and M represents the tap length. The superscript “T” denotes a transposed matrix. When the CMA method is used, these tap coefficients are controlled on the basis of the formulae (12) to (15) described in Non Patent Literature 1. The X-polarization input and Y-polarization input are weighted and summed by using the coefficients controlled by the CMA method. This enables deteriorating factors dependent on the polarization to be cancelled, and the compensation process is accomplished. As a result, proper receiving processes can be realized.
Thus, the butterfly-structured FIR filter is employed in the coherent receiving system using the digital signal processing. If the tap length of the FIR filter increases, the calculation amount necessary for updating the tap coefficients increases accordingly and this requires a large amount of circuit resources. It is desirable, therefore, to shorten the tap length of the FIR filter as much as possible. On the other hand, in order to compensate a temporal spread of a signal due to the polarization mode dispersion by using the butterfly-structured FIR filter, it is necessary to realize an inverse response of the temporal spread by means of the FIR filter. If the tap length of the FIR filter is finite, however, there is a possibility that an intended response cannot be realized.
Non Patent Literature 2 describes an example of the polarization demultiplexing in a coherent receiver which is performed by controlling the coefficients of a butterfly-structured FIR filter using the CMA method. As described in Non Patent Literature 2, in general, a response of the polarization mode dispersion, which is a main factor to be compensated by a butterfly-structured FIR filter, can be expressed by a unitary matrix, and so the inverse response can also be expressed by a unitary matrix. Accordingly, the following relation holds for the inverse response.hyy(t)=hxx*(−t),hxy(t)=−hy*(−t)  (3)
Here, the superscript “*” represents a complex conjugate. From the relation of formula (3), the following formulae hold:|hxx(t)|2+|hyy(t)|2=|hxx(−t)|2+|hyy(−t)|2  (4)|hxy(t)|2+|hyx(t)|2=|hxy(−t)|2+|hyx(−t)|  (5)
As can been seen from formulae (4) and (5), the magnitude of the inverse response of the polarization mode dispersion has a kind of temporal centrosymmetry. In a case where the tap coefficients of a butterfly-structured FIR filter are adaptively controlled, taking the above relationship into account, initial values of the tap coefficients are generally set so that significant coefficients may be allocated for the center tap of the FIR filter and the other coefficients may be set to “0”. Here, the significant coefficients correspond to a Jones matrix representing input-output relations for respective polarization signals, which is realized by the butterfly-structured FIR filter. As described in Non Patent Literature 2, for example, the initial values of the tap coefficients of the butterfly-structured FIR filter can be set as follows:hxx=[0001000],hxy=[0000000],hyx=[0000000],hyy=[0001000]
Here, it is assumed that the polarization rotation and temporal spread due to the transmission do not arise initially, and the tap length M is set at 7. In this example, an identical Jones matrix expressed by the following formula (6) is set at hxx(3), hxy(3), hyx(3), and hyy(3) of central tap coefficients in the FIR filter.
                              (                                                                                          h                    xx                                    ⁡                                      (                    3                    )                                                                                                                    h                    xy                                    ⁡                                      (                    3                    )                                                                                                                                            h                    yx                                    ⁡                                      (                    3                    )                                                                                                                                          h                      yy                                        ⁡                                          (                      3                      )                                                        ⁢                                                                                                                      )                =                  (                                                    1                                            0                                                                    0                                            1                                              )                                    (        6        )            
Then, it is possible to perform the adaptive equalization signal processing by using tap coefficients which have converged by means of the CMA method.
On the other hand, Patent Literature 1 describes an example of a compensation device to compensate a distortion having occurred in an optical fiber by using optical elements. The related compensation device described in Patent Literature 1 includes a wide-band adaptive optical equalizer, an optical feedback monitor, and a controller. The wide-band adaptive optical equalizer includes a plurality of tunable optical filter units, each of which includes a beam splitter and a differential delay element. The optical feedback monitor samples signals passing through the wide-band adaptive optical equalizer. It is said that the controller sets initial control parameters of the tunable optical filter unit and controls the wide-band adaptive optical equalizer by using the control parameters which are determined on the basis of sampling results of the optical feedback monitor. However, since the polarization mode dispersion varies temporally and it is difficult for the optical element to track the variation, it is difficult for the related compensation device to compensate the polarization mode dispersion.
Patent Literature 1: Japanese Patent Application Laid-Open Publication (Translation of PCT Application) No. 2005-520391 (paragraphs [0047] to [0087])
Non Patent Literature 1: S. J. Savory, “Digital filters for coherent optical receivers,” Optics Express Vol. 16, No. 2, 2008, pp. 804-817.
Non Patent Literature 2: L. Liu et al., “Initial Tap Setup of Constant Modulus Algorithm for Polarization De-multiplexing in Optical Coherent Receivers,” Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper OMT2.